Comparison of Variable Speed Wind
Turbine Control Strategies
S. Arnaltes
Department of Electrical Engineering
Escuela Politécnica Superior, Universidad Carlos III de Madrid
Avda. Universidad 30, 28911 Leganés (Spain)
phone:+34 916 249911, fax:+34 916 249430, e-mail: [email protected]
the optimal tip speed ratio [2]. Of course, instead of a
torque reference, a power reference can also be obtained
[3, 4]. Speed-mode control is based on obtaining a
rotational speed reference that leads to the optimal tip
speed ratio, thus a speed control loop is required. There
are different approaches to obtaining this speed reference.
A wind speed measurement can be used to derive the
rotational speed reference [5]. The disadvantage of this
method is that an anemometer is required, which
measures only the wind velocity at one point of the rotor,
and also this measurement is affected by the rotor wake.
An estimation of the wind velocity can be used instead
[6]. Another speed-mode control alternative consists of
obtaining the rotational speed reference from a power (or
torque) - speed characteristic that leads to the optimal tip
speed ratio. This method has the disadvantage of
requiring a wind turbine torque observer [7], although
generator torque (or power) can also be used, but
rotational speed reference will be the optimal only at
steady state. Finally, the speed reference that maximize
the turbine power can be obtained through a fuzzy logic
based search as in [8].
Abstract.
Variable speed operation of wind turbines
presents certain advantages over constant speed operation.
Basically, variable speed wind turbines use the high inertia of
the rotating mechanical parts of the system as a flywheel; this
helps to smooth power fluctuations and reduces the drive train
mechanical stress. Also, variable speed systems could lead to
maximise the capture of energy during partial load operation. In
this paper alternative control strategies for variable speed
operation are considered and compared from the point of view
of energy yield and power quality. Control aim is always
maximum power generation. Maximum power tracking and
power fluctuation will be analysed when exciting the different
configurations with a particular wind profile. Also fixed speed
wind turbine are considered for the comparison.
Key words
wind energy, power quality, flicker, wind turbine control.
1.
Introduction
Early wind energy conversion systems were based on
generators directly connected to the grid, hence the speed
of these systems was constant (with synchronous
generators) or quasi-constant (with asynchronous
generators). The evolution of power semiconductors has
contributed enormously to variable speed wind energy
conversion systems by interfacing the constant frequency
of the grid to the variable frequency of the generator.
For wind velocities higher than rated, the capture of
energy by the turbine must be limited by stall or pitch
control. For the following only wind velocities bellow
rated are considered, as only in that range of velocities
maximum power can be achieved.
2. Variable speed control strategies
Variable speed operation of wind turbines demands the
application of variable speed generators operating on the
constant frequency of the grid. Different types of
generators can be used, usually induction generators
(with cage or wound rotor) or synchronous generators
(with field winding or permanent magnets); all of them
require the use of a suitable electronic power converter.
The aerodynamic power of a wind turbine is given by the
equation:
P=
Different control strategies have been proposed in the
literature for variable speed operation, but a possible
classification could lead to the so-called speed-mode
control and torque-mode control [1]. Torque-mode
control consists of obtaining an electrical torque
reference from the shaft speed measurement that leads to
1
2
2 3
ρπR v c p
(1)
where ρ is the air density, R the turbine radius, v the wind
speed and cp the power coefficient.
The power coefficient is defined as the ratio of turbine
power to wind power, and it is a function of the tip speed
ratio (λ) as well as the blade pitch angle (β). For the
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following β is considered constant, as it changes only
when full load is achieved through a feedback control
loop that regulates power output. λ is defined as the ratio
of turbine speed at the tip of a blade to wind velocity, and
given by:
λ=
where Ωopt is a function of wind speed:
Ω opt =
λ opt ⋅ v
R
(4)
then
R⋅Ω
(2)
v
3
Pmax = K ⋅ Ω
opt
where Ω is the turbine speed. In a typical wind turbine
with a fixed β, function cp(λ) shows (figure 1) that there
is an optimum value of tip speed ratio (λopt) that makes
power coefficient maximum (cp,max). Figure 2 shows the
turbine power-speed characteristics for various wind
velocity values.
(5)
or, by dividing both terms of (5) by Ωopt
2
T
= K ⋅Ω
opt
opt
(6)
where
K =
0.5
1
2
ρπR
5 c p ,max
λ
opt
(7)
0.4
Power coeficient C
P
Expression (5) shows that maximum power a particular
turbine can extract from wind is a cubic function of the
turbine optimum speed (figure 2). Expression 6 shows
the relationship between torque and speed at the
maximum power point of operation.
0.3
0.2
Two control strategies for capturing the maximum power
from a particular wind are going to be considered: speedmode control and torque-mode control.
0.1
0
0
2
4
6
8
10
12
14
16
18
20
A. Speed-mode control
tip speed ratio λ
Expression (2) shows that for extracting maximum power
from a particular wind, control has to adjust turbine speed
so that optimum tip speed ratio (λopt) is always obtained.
Fig. 1. Function cp(λ)
1.5
Electrical output P/P
n
P
Cp,max
Speed reference that achieves maximum power can be
obtained in different ways. First, it can be obtained from
the measurement of wind velocity by using (4), but an
anemometer is required, which measures only the wind
velocity at one point of the rotor, and also this
measurement is affected by the rotor wake.
1
14 m/s
13
12
11
0.5
An estimation of wind velocity as seen by the whole
turbine rotor can be used. At the maximum power point
rotational speed and wind velocity are related by
expression (4). Then optimal speed can be obtained
directly from (6) as:
10
9
8
0
0
0.5
1
1.5
speed n/n
2
2.5
3
n
Ω
Fig. 2. Power-speed characteristics
By eliminating wind speed from (1) y (2), when power
coefficient is maximum:
3
 R⋅Ω 
1
opt 
2
(3)
Pmax = ρπR
c p,max

2
 λ opt 


opt
=
Tˆ
t
K
(8)
where Tˆt is an estimation of the turbine torque. This
method presents the disadvantage of requiring a turbine
torque observer.
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In steady state, turbine torque is equal to generator
torque, so if maximum power tracking is only an
objective in steady state, then optimal speed can be
obtained from (5) using generator power output as input:
P
3 g
Ω
=
opt
K
T
g
= K ⋅Ω
2
(10)
Figure 4 shows the system block diagram, here for a
particular wind velocity (lower than rated), an
electromagnetic torque reference that achieves maximum
power is given to the inner torque control loop. If wind
velocity increases suddenly there will be an increase of
turbine torque, and because turbine speed can not change
instantaneously, from the above expression generator
torque will remain the same, resulting in an accelerating
torque until the new optimal point of operation is
achieved.
(9)
This method has the advantage of using generator power
as input, which is a variable that can be easily measured
(in fact it is measured for other control functions).
Figure 3 shows the system block diagram. Here for a
particular wind velocity (lower than rated), a speed
reference that achieves maximum power is given to a
speed control loop. The speed controller will set a torque
reference to the electrical generator. Balance between
turbine torque and generator torque will result in an
accelerating (or decelerating) torque until desired speed
is achieved. A subordinated torque control loop will
control generator torque by acting on the proper variable,
depending on the generator type.
Fig. 4. Torque mode control block diagram
3. Simulation Results
A comparative analysis of the aforementioned control
strategies is going to be carried out by using simulation
results. To compare simulation results the following
characteristics are used: maximum power tracking and
power quality. These characteristics are quantified as
follows:
Fig. 3. Speed mode control block diagram
•
Speed-mode control assures a fast tracking of maximum
power if a high bandwidth speed control loop is used, but
as it will be shown later, although energy capture is
maximised the results are not so good from the power
quality point of view.
•
Maximum power tracking is evaluated as the energy
yield during simulation time.
Power quality is evaluated as generator power output
standard deviation.
For the comparative analysis four cases are considered:
B. Torque- mode control
•
•
•
Expression (6) shows the relationship between torque and
speed at the maximum power point. Then, in order to
obtain the turbine optimal torque, control has to adjust
the generator torque reference so that maximum power is
obtained. In steady state turbine torque is equal to
generator torque. Then, maximum power can be achieved
by demanding an electrical torque from the generator as:
Case 1: fixed speed wind turbine.
Case 2: torque mode control strategy.
Case 3, a and b: speed mode control strategy.
As it has already been said, a speed controller is needed
when the wind turbine is being operated in the speed
mode control. This controller is going to affect greatly
the dynamic behaviour of the whole system. So, special
attention is going to be paid to the design of the speed
controller. A PI controller has been chosen for the speed
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control loop. For the comparative analysis two
controllers have been designed (cases a and b), both have
been designed to provide the same phase margin, but they
differ in the resulting speed control loop bandwidth. The
parameters of both controllers and the resulting
characteristics of the control loops are given in Table I.
From figures, it seems that speed mode control of
variable speed wind turbines produces even more power
fluctuations than fixed speed wind turbines, and the
higher the controller bandwidth the higher the power
fluctuations. Obviously, the best power response is
obtained in case 2, where torque mode control of a
variable speed wind turbine is used. When integrating
power output in the studied time interval, energy yield in
that period is obtained (see table III). Energy capture is
higher in case 3b, when turbine speed follows wind
velocity more accurately, and energy capture is obviously
lower in case 1, when fixed speed wind turbine is used.
Table I. Speed control loop parameters and characteristics
PI
Proportional Integral
Phase
Bandwidth
Controller
Gain
Gain
Margin
Case a
10.94
7.76
65º
2 rad/s
Case b
22.04
31.04
65º
4 rad/s
System response will be obtained when exciting the wind
turbine with a particular wind profile. This wind profile,
given in figure 5, represents the wind velocity on the
turbine rotor as measured by an anemometer.
Fig. 6. Simulation results (case 1)
Fig. 5. Wind profile
The parameters of the wind turbine and the wind profile
are given in Table II.
Table II. Turbine and wind profile characteristics
Turbine radius
25.85 m
Rated power
1 MW
Rated rotational speed
26.6 rpm
Inertia constant
3.88 s
Rated wind velocity
12 m/s
Mean wind velocity
7.5 m/s
Turbulence intensity
0.244
A.
Maximum power tracking analysis
Fig. 7. Simulation results (case 2)
Figures 6, 7, 8 and 9 show system responses in cases 1, 2,
3a y 3b, respectively. In figures, rotational speed
response is shown in red, while power output response is
shown in magenta. Obviously, speed is nearly constant in
case 1, while in cases 2 and 3 rotational speed tends to
follow wind velocity variations. Figures show that the
dynamic tracking of maximum power is better in speed
mode control than in torque mode control, and also that
the higher the controller bandwidth the better the
tracking. Nevertheless, as a consequence of this,
generator torque oscillations, imposed by the speed
controller for achieving optimal tip speed ratio, are going
to affect power output fluctuations.
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PCC. For this reason, the evaluation of flicker emission
by wind turbines is based on current, or power,
measurements instead of voltage.
Voltage fluctuations ∆U at PCC are related to power
fluctuations according to:
∆U =
P⋅R+Q⋅ X
U
(10)
where P and Q are, respectively, the active and reactive
power injected into the grid by the wind turbine generator
(figure 10) and R and X are, respectively, the shortcircuit
resistance and reactance of the grid.
Fig. 8. Simulation results (case 3a)
Fig. 9. Simulation results (case 3b)
Fig. 10. Grid connected wind turbine generator
Nevertheless, energy yield and hence the deviation from
maximum power coefficient depends on the shape of the
cp-λ curve. With a sharp characteristic a significant
increase in energy capture can be obtained when a good
power tracking control method is employed.
Voltage fluctuations at the PCC can be used to calculate
short term flicker severity, Pst, by using a flickermeter
that complies with the IEC 61000-4-15.
B.
In this subsection, Pst is not going to be used for the
comparative analysis but only power fluctuations, as this
is enough for reaching the conclusions of this subsection.
Note that generally speaking, for a particular grid, higher
power fluctuations will cause higher voltage fluctuations
and therefore higher flicker emissions.
Power quality analysis
As shown in figures 6, 7, 8 and 9, wind turbines produce
a power output that is not constant due to wind
variations. Power oscillations produce voltage
fluctuations at the point of common coupling (PCC),
which increase with the turbulence intensity. Voltage
flicker can become a limiting factor for connecting wind
turbines at weak networks, and even on relatively strong
networks with a high wind power installed capacity.
Power fluctuations are going to be quantified by
calculating the ratio of standard deviation to mean value
of power response in the considered cases. Results are
given in table III. From these results, it is clear that
torque mode control strategy is better than speed mode
control strategy, because it results in lower power
fluctuations. Also, the higher the controller bandwidth
the higher power fluctuations are obtained.
Variable speed wind turbines can improve many aspects
of power quality in distribution grids due to the reduction
of short-term power fluctuations that results in a
reduction of flicker. Also, reactive power can be
controlled in variable speed wind turbines which helps to
improve power quality.
Table III. Energy yield and power fluctuations
Mean power output Standard deviation /
mean output
Case 1
256.2 kW
0.8975
Case 2
286.1 kW
0.6396
Case 3a
295.1 kW
1.0302
Case 3b
298.6 kW
1.1217
Measuring flicker at the PCC has the disadvantage that
the measurement include the contribution to the flicker
produced by other equipment connected to the same
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4. Conclusions
References
Variable speed wind turbines feature higher energy yields
and lower power fluctuations than fixed speed wind
turbines. The last feature is particularly important as
flicker may become a limitation to wind generation on
power systems. Also, variable speed wind turbines
produce more reduced loads in the mechanical parts than
fixed speed wind turbines, but this analysis has not been
carried out in this paper.
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When comparing torque mode control and speed mode
control strategies, simulation results shows that speed
mode control strategy follows wind speed, in order to
achieve maximum power coefficient, more accurately,
i.e., it is more adequate for fast maximum power
tracking, and the higher the speed control loop bandwidth
is, the better the tracking is. Nevertheless, as a
consequence, it produces more power fluctuations, since
speed is rigidly imposed to the turbine. So, from power
quality point of view, torque mode control strategy
presents better behaviour, because speed is not directly
imposed to the turbine and this control strategy lets the
wind turbine to freely change rotational speed during the
transient.
Acknowledgement
Author wish to acknowledge the support of the Spanish
Ministerio de Ciencia y Tecnología under project no.
DPI2002-04555-C04-03.
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